Control of a rolling process is to roll a material so that the rolled material after completion of manufacturing has desired dimensions and temperature. Rolling process control generally includes setup control and dynamic control. In the setup control, a rolling phenomenon is predicted by a model expression, and a setting value of equipment of a rolling facility, such as a rolling speed, an amount of cooling water, and a roll gap of a rolling mill, is decided so that the rolled material has the desired dimensions and temperature. However, the model expression cannot completely represent the physical phenomena that occur in the rolling process. In addition, a calculation expression that represents a model is simplified for reasons of reduction of a calculation load, convenience of adjustment, etc. For this reason, a deviation is generated between a result value measured by a sensor and a prediction value calculated by the model expression. Consequently, in conventional setup control of the rolling process, in order to achieve improvement and stability of prediction accuracy of the rolling phenomenon, learning control is performed in which a learning coefficient is provided in the model expression, and in which the learning coefficient is automatically adjusted based on result data. A finishing temperature and a rolling load are included in the result data, and they are collected regarding an aiming point of setup calculation.
Here, a summary of general learning control of a rolling process will be explained. The learning control includes a plurality of processes, and one of them is result recalculation. In the result recalculation, a model prediction value based on result data is calculated using a model expression. This is generally called a result recalculation value. The result recalculation value is compared with a result value included in the result data, and an error of the result recalculation value with respect to the result value, i.e. a model error, is calculated. For example, in a case of setup control of a roll gap of a rolling mill, a result value of a rolling load measured in a load cell is compared with the result recalculation value of the rolling load calculated from the result data using the model expression, and the model error of the rolling load is calculated.
A learning coefficient is then calculated based on the model error. The learning coefficient calculated at this time is called an instantaneous value of the learning coefficient. However, since it is unknown which factor causes the model error among factors ignored in simplifying and constructing the model expression, and disturbance and an error are included in the result data itself used for learning, the instantaneous value of the learning coefficient calculated from the model error cannot be applied to a next rolled material as it is. Consequently, it is performed to make the instantaneous value of the learning coefficient pass through a smoothing filter. A value obtained by smoothing the instantaneous value of the learning coefficient is used as an update value of the learning coefficient.
The following expression is a specific example of an expression of the smoothing filter that calculates the update value from the instantaneous value of the learning coefficient. A deviation between the instantaneous value of the learning coefficient and a previous value (the previous value of the update value) of the learning coefficient is multiplied by an update gain, and the previous value of the learning coefficient is added to a value obtained by the multiplication, whereby the update value of the learning coefficient is calculated.Znew=Zuse*(1−α)+Zcur*αWhere, Znew: Learning coefficient update value
Zcur: Learning coefficient (Instantaneous value)
Zuse: Learning coefficient (Previous value)
α: Learning coefficient update gain (Time constant of filter)
The calculated update value of the learning coefficient is generally recorded in a stratified table. Stratification is a concept for dividing rolling conditions, such as a thickness, a width, a strain, a strain rate, and a temperature of a rolled material. For example, when the thickness is divided into m, and the width into n, the stratified table includes m×n cells. Whenever rolling of the material is ended, the update value of the learning coefficient is calculated, and is recorded in a cell coincident with rolling conditions of the material. The learning coefficient different for each rolling condition can be appropriately managed by using the stratified table for recording the learning coefficient, and prediction accuracy of a rolling phenomenon is improved. That is, learning control using the stratified table is an important function to secure prediction accuracy of the rolling phenomenon of the model expression and to thereby secure quality accuracy of a product and stability of rolling.
However, there is also a problem in the learning control using the stratified table. The learning coefficient is managed by the stratified table, and thereby the learning coefficient is managed in one corresponding cell in the stratified table, and is smoothed and updated for each corresponding cell. For this reason, a number of rolling chances (number of rollings) are needed for the learning coefficient of one cell to be saturated. In addition, since a different cell number is selected if there is even a slight difference in a rolling condition, a learning coefficient of a different cell is newly updated. For this reason, a number of rolling chances are needed for each cell for all the cells included in the stratified table.
As one idea to reduce necessary rolling chances, a method can be considered in which when a learning coefficient of one cell is updated, a learning coefficient of an adjacent cell is also simultaneously updated. In this learning method, as shown in the following expression, the learning coefficient is calculated by the same method as mentioned above with respect to a cell (i, j) corresponding to present rolling conditions. Note that (i,j) indicates a coordinate of the corresponding cell in the stratified table.Znew(i,j)=Zuse(i,j)*(1−α)+Zcur(i,j)*αWhere, Znew(i, j): Learning coefficient update value of corresponding cell
Zcur(i, j): Learning coefficient (Instantaneous value) of corresponding cell
Zuse(i, j): Learning coefficient (Previous value) of corresponding cell
α: Learning coefficient update gain (Time constant of filter) of corresponding cell
A learning coefficient is calculated by the following expression with respect to an adjacent cell (p, q). Note that (p, q) indicates a coordinate of the adjacent cell in the stratified table, which includes (i−1, j), (i, j−1), (i+1, j), and (i+1, j).Znew(p,q)=Zuse(p,q)*(1−α′)+Zcur(i,j)*α′Where, Znew(p, q): Learning coefficient update value of adjacent cell
Zcur(i, j): Learning coefficient (Instantaneous value) of corresponding cell
Zuse(p, q): Learning coefficient (Previous value) of adjacent cell
α′: Learning coefficient update gain (Time constant of filter) of adjacent cell
According to the learning method, the learning coefficient of the adjacent cell can be saturated with the fewest possible rolling chances. However, although learning of the adjacent cell proceeds, a learning coefficient of a cell a little away from the corresponding cell cannot be updated. That is, with the learning method, only a limited effect can be obtained regarding reduction of the rolling chances. In addition, when the learning coefficient of the corresponding cell is unstable, and fluctuation is large on each updating, the learning coefficient of the adjacent cell is also affected by the instability.
Further, there is also another problem in the learning control using the stratified table. The problem is that the learning control is hard to follow temporal change of the rolling process since the cell is subdivided. When there is no rolling for a while regarding rolling conditions corresponding to a certain cell, the rolling process may change in the meantime. Change of the rolling process described here includes both active change, such as change in temperature level in hot rolling and passive change, such as deterioration of facility. If the rolling process changes, change occurs also in a true learning coefficient. For this reason, when the update value of the learning coefficient recorded in the stratified table remains old, the value is probably not an appropriate one. When the learning coefficient that is not the appropriate value is applied to the model expression, an error included in a model prediction value becomes large to thereby reduce accuracy of the setting value of the equipment.
As described above, there are various problems in the learning control using the conventionally generally used stratified table. Meanwhile, there are also present proposals disclosed in the following PTLs 1 and 2 in the learning control using the stratified table.
The proposal disclosed in PTL 1 is a method for separating a gap by time-series fluctuation included in a gap between a model and a phenomenon as a time-series learning coefficient. The learning coefficients corresponding to the present rolling conditions are calculated by separating them into grouped learning coefficients depending on the rolling phenomenon and the time-series learning coefficients depending on temporal change, a model prediction value is corrected based on these two types of learning coefficients, and thereby accuracy of the model prediction value is improved. Specifically, an update value of the time-series learning coefficient is calculated using a smoothing filter based on an instantaneous value of the learning coefficient calculated from a model error, and a use value of the learning coefficient in connection with the rolling phenomenon in the present rolling conditions. The update value of the learning coefficient in connection with the rolling phenomenon in the present rolling conditions is then calculated using the smoothing filter based on a value that remains after removing the update value of the time-series learning coefficient from the instantaneous value of the learning coefficient.
According to the learning method proposed in PTL 1, the gap by time-series fluctuation of a process line can be extracted as the time-series learning coefficient. However, the grouped learning coefficient dependent on the rolling phenomenon is calculated for each cell even in the learning method. For this reason, even if the rolling process is changed while rolling by certain rolling conditions is not performed for a while, and thereby fluctuation occurs in a gap between a model and a phenomenon in the present rolling conditions, the fluctuation is not reflected in a learning coefficient recorded in a cell of the present rolling conditions. Consequently, a learning coefficient in which the gap between the model and the phenomenon has been appropriately corrected cannot be obtained in the first rolling in the present rolling conditions after the change of the rolling process.
A proposal disclosed in PTL 2 is a method in which a learning term of a model expression is recorded for each lot (cell) corresponding to a division of a rolled material, and a learning level of a learning term corresponding to a next lot is determined whenever the lot is changed, and in which if the learning level is lower than a criterion, the learning term of the next lot is corrected using a learning term of the other lot having a high learning level. Specifically, the learning level of the learning term of the next lot is determined on the basis of whether a learning frequency of the learning term of the next lot is not less than a reference frequency, and of whether a standard deviation of the most recent predetermined time of the learning term corresponding to the next lot is not more than a reference value. If the learning level is then lower than the criterion, correction of the learning term of the lot is performed using a smoothing filter based on a learning term of each lot adjacent to the lot on the table, and a correction coefficient decided according to the learning level.
According to the learning method proposed in PTL 2, even though the learning term of the next lot is unlearned, the unlearned learning term of the lot can be optimized using the learned learning term of the adjacent lot. However, the learning term of the adjacent lot is not necessarily more learned than the learning term of the next lot. When the learning term of the next lot is unlearned, and the learning term of the adjacent lot is also unlearned, setup calculation must be performed regarding the next lot based on the unlearned learning term. In addition, when the learning term of the adjacent lot is unstable, i.e. when a value largely fluctuates on each updating, the learning term of the next lot corrected using the learning term of the adjacent lot also becomes unstable. Further, when accuracy of the learning term of the adjacent lot has deteriorated with elapse of time due to change of the rolling process while rolling is not performed for a while, accuracy of the learning term of the next lot corrected using the learning term of the adjacent lot also deteriorates.